From the <del> spec:
This value may be shown to the user, but it is primarily intended for private use.
As it can be shown to the user, why not always use <del> instead of <s>? More importantly for us, why should Markdown support both? If there is no practical reason, I suggest only supporting <del> via ~~ and saving a lot of confusion.
I may be mistaken, but <s> feels like a legacy element in the same way that <b>, <i>, and <u> do.